Apparatus for forming surfaces of revolution



July 9, 1946, c. B. MADDO CK APPAfiATUS FOR FORMING SURFACES OF REVOLUTION Filed July 20, 1939 5 Sheets-Sheet l M Mwzm/a,

July 9, 1946. c. B. MADDOCK APPARATUS FOR FORMING SURFACES OF REVOLUTION Filed July 20. 1959 5 Sheets-Sheet 2 AI/lvum .w snoos 01 g 3 g m w 5 July 9, 1946. c. B. MADDOCK APPARATUS FOR FORMING SURFACES OF REVOLUTION Filed Jui 20, 1959 5 Sheets-Sheet 5 July 9, 1946. c. B. MADDOCK 68 APPARATUS FOR FORMING SURFACES OF REVOLUTION Filed July 20, 1959 5 Shets-Sheet 4 Avail! VI m I H I] 5 02 July 9, 1946. c. B. MAl DDOCK APPARATUS FOR FORMING SURFACES OF REVOLUTION 1 "Filed July 20, 1959 5 Sheets-sheaf 5 Patented July 9, 1946 APPsRATUsFoR FORMING SURFACESOF REVOLUTION Y Charles B. Maddock, St. Louis, Mo., assignor to Baker"& Company; Inc., Newark, N. J., a corporation' of New Jersey Application July 20, 1939, Serial No. 285,482 I 22 Claims. (01. 82-511) 1 v[Ih'i'sinvention relates toapparatus for. forming surfaces of revolution "having conic, longitudinal sections, and with regard tocertain more Specific features, to apparatusjo-f the class described which will form paraboloids. v

' Among the several objects of the invention may be noted the provision of apparatus for forming paraboloids and the likewhich accomplishes the desired result with a high degree of overall accuracyfbu't particularly ina region where prior apparatus 'failed, namely, near the vertex} and the provision of apparatus of the class described which will reduce the cost of high-accuracy products such assearchlight, telescopic and other reflectors and permitthemto beft'urned out satis- I"a'ctorily invquantity; Other objects will be in 'pa'rtobvious' and in part pointed out hereinafter.

The invention accordingly comprises the'elej- .ments and combinations of elements, features ,of

construction, and arrangements of parts which;

will be exemplified in the structures hereinafter described, and the scope of the application of which will be indicate'diin the following claims.

In the accompanying'drawings, in which are illustrated several various possible embodiments ofthe'i'nvention,

" Fig..1'is a diagram, illustrating certain basic geometric concepts,"

Fig.2 is a geometric diagranisimilar to 1 but showing superimposed ajkinernatic. diagram;

Fig. '3 isa View similar 'to Fig 2, but shown on an enlarged scale and illustrating additional kinematicfeature's of a 'bisecting mechanis'm;

Fig. '4 is a plan view of the mechanism applied to a lathe embodying the principles of the inven,-.

tionfthe view beingtaken on line 4- 4 of Fig. 5

.so as to maintain all projections orthographic; Fig. 5 is a vertical section taken on line 5-5 Fig. 6 is a fragmentary enlarged plan view of tain operating parts removed and an alignment jig shown in position; and, 7 a V I v a Fig. 12 is a verticals'ectiont'aken on line I2l 2 01mg. 11. j I v .1

Similar reference characters indicate corresponding" parts throughout the several views .of the drawings.

Oneway in which to cut or spinor similarly form a paraboloid or the'like is jto mount the material from which it is to be made upon a. rotary device such as alathe and then" work upon a it with suitable tools, using a template as a guide.

This procedure. is essentially no more accurate than the template. The template in turn depends upon manual operation for its accuracy,

and the accuracy of manual operations obviously isnot consistent at all times. p f

Various linkages have been suggested for forming conicsurfaces of revolution, such as paraboloids; ellipsoids and 'hyperboloids, but they are open to ,a' commondefect, namely that thecutting or forming tool, as it proceeds through its operations, has a varying angular aspect with respect to the curved. longitudinal section desired. {This means that, "ifthe cutting edge of the tool is anything except a p nt, inherent inaccuracies are introduced into the surface. For example, if a point is used at,v the; end of the forming tool, in order to'eliminate the undesireration" f In order to provide a smooth finish, a cutting or'forming tool ordinarilymu'st have a convex or curvilinear cutting edge rathenthan a theoretical point, cutting or forming edge or end. 'Such an edgeorend permits of approaching with one operation more closely to the final finish desired without any, or at least' 'only an easy, finishing operation. I

The present invention'n'ot only provides an improved linkage for moving a cutting or, forming tool generally, but includes a mechanism for maintaining the tool at the proper aspect angle with respect to the surface to be worked, so that the desired edge may be employed for smooth h. r

In orderthat the invention may be better understood; some theoretical aspects of the outlinmg? of p'arabolas In a plane will first be discussed. 7 j

1 is shown a set ofrectangular coordinates onjX-Y axes; If a width W and a height H'be assumed for, a desired parabola P, the vertex-will" be at'V, and theparabola'may be ;con-

3 structed geometrically by using this vertex V as a pole and employing radial lines R as follows:

The horizontal axis is divided into a predetermined number of equal divisions, for example, eight on each side of the center of the figure, as shown. The vertical or Y axis is divided into an equal number of divisions (of equal or different size) above the X axis. The radial lines R are then drawn from the vertex V to the respective vertical edge divisions |8. Where these respective radial lines cross the respective horizontal division lines |-8', intercepts K are determined which form the locus of the desired parabola, as shown.

Th focus F of this parabola P ma be found by known methods, and it is as indicated in the drawings. It is not necessarily on the exact axis, but has been so chosen in the present example,

From the above it will be clear that if a point proceeds along the parabola, and at the same time the drawing plane is rotated, aparaboloid of revolution will theoretically be generated in the space manifold of that plane.

. Furthermore, by laying off equal distances D parallelto the Y axis, a second parabola P2 will be determined, which is the same as P but simply displaced the distance D. The focus F2 of this parabola P2 will be displaced from the focus F an equal distance D.

It will also be clear that if a cutting tool such as illustrated at T be moved with its center line CL parallel to itself, a theoretical cutting point ill thereon will generate a paraboloid of revolution in a solid if said solid be turned relatively around the Y axis shown. Thus, it will be'seen in which such an improper aspect of thetool can be avoided is always to maintain the desiredface N of the tool tangent to the curve P2 at point |ll.. This involves varying the angle of the center One of the advantages of this inventionconsists in causing said tool to angle properly to maintain a constant aspect of the cutting tool line of'the toolxas it traverses the curve, P2

face such as N, as indicated for example at N, J

wherein a constant tangency is always main- '1,

tained at a center point I0. By this means very fine, broad finishing cuts may be taken, providing mirror-like surfaces of great accuracy with out consequential circular or spiral ridges therein, as would occur with a point cutting tool.

In the above method for generating the parabola P2 (which may be considered as a section of the desired paraboloid of revolution) ,the motions of the coordinates of the loci K along the XY axis are proportional.

In Fig. 2 is shown the part of the mechanism of the invention which traces by means of a point the geometric construction outlin inconnection with Fig, 1. In this figure is shown the theoretical parabola P generated by what will H 33 and supportsa rotary slider I5. The slideris slidable upon a radius rod |9 pivoted at the vertex V. The rod includes a guide 2| surrounding a pin 23 on a coordinate slider 25. The slider 25 moves parallel to the Y axis in a longitudinal guide 21.

At right'angles to the guide 21 is a guide 29 corresponding to the X axis hereinbefore described. In the guide 29 is a slider 3|, which slides at right angles to the slider 25.

Various ways may be used for coordinating the desired proportional movements between the sliders 25 and 3|. For the purpose of the diagrammatic Fig. 2, I have illustrated these coordinator blocks 25 and 3| as driven b lead screws 35 and 31, geared at 39 in the ratio of 1:2 respectively,

- so that the screw 31 travels faster but proportionally to the screw 35, thus moving the block 3| throughout its range of movement which in the examplechosen is double the range of movement of the block 25.

From the above it will be seen that, if the screw 35 is driven, the screw 31 moving in relation thereto, the pin 23 will assume at successively equal time intervals successive equal intervals on the Y axis. At the same time the'block 3| will assume proportional positions at equal intervals on the X axis. Thus, the center line of the tool holder 33 becomes positioned at successive equal intervals along the X axis. The intersection ll 'of the center line of the radius rod IS with the center line of the'tool holder 33 fulfills the necessary conditions referred to in connection with Fig. l.

The above construction solves the problem of providing a mechanism to drive a theoretical point such as H along a parabola P. However, since it is impracticable to place a cutting tool at the point H which is already occupied by a pin, it is necessary to project the actual cutting tool beyond the point I and to generate at point CP a parallel parabola P2, the actual focus of which is at F-2. If the tool holder 33 were merely extended to a point CP, as shown, it would in its various lateral positions assume, with respect to the parabola P2, various and different angular aspects which have been above designated as undesirable. That is, the problem could not be successfully solved by simply providing a pointed tool on the tool holder 33 extending so that its point is on the parabola P2, because point C-P needs to remain clear for cutting within a bowl-shaped surface, it cannot be used as a point for a pivot pin, and rotation of the block 4| around the center CP is therefore managed by arranging a circular slide 43 to work in 'a circular guide 45 in the tool holder 33. The radii of the circular forms for the parts '43 and 45 have centers at CP.

At the actual focus F2 of the parabola.P2 is provided a pin 51. This pin is in aguide E9 of a drag link 5|. The center line of the link 5| passes through the focus P2 and point C-P.

The link5l is made rotary about the center Cl? by providing it with a circular slide 53 .in a circular guide 55 of the tool holder 33.

Connected between the tool holder 33 and the "drag link .5I are bisecting links 51 and.59 respectively. The" links'51v and 59 are pivoted in common to a pin! which works in a'slot 63 on the center line of-the tool blockJI.

' From the above it will be clear that, as the tool holder 33 "moves (under "the influence of the coordinator blocks 25. and 3| and radius rod I9), the center line ofthe block 4| will-always bisect the angle formed by the centerlines of the tool v holder 33 and the drag link'5I. This bisecting center line will always pass through the cutting pbintC-P, and thus the arcuate face of the tool 'Talways remains with afixed aspect'with respect to the parabola,that is, the tool holder face and "the face of the parabola always have. coincidental normals G to commonv tangents H at C-P, re-

gardless of the position of C--P onthe desired parabola.

It will be understood that the geometric and kinematic showings of Figs. i-3 are diagrammatic 'andxthat the various mechanical pairs are illustrated symbolically. In the remaining figuresof the case is shown actualapparatus for carrying out the principles describedtin connection with Figs; l-3, and so'far as possible similar reference characters and description ofparts will be used. It should be noted, however, that the lead screw and gear drive for theJcoordinator blocks Hand 3]. (shown in Figs. 2 and 3) are not'used inthe remaining figures, a set of ninety-degree, phased dle, andhas the usual gear train 6| from the live spindle to a splined'lead' screw 63, thelatter passing through the'control apron 84 of the .car-

riage 55. ,;;The .screw' 63, among other things, 1 serves to furnish, through the;usual clutchland ;gear,train in the apro'n IiA, .a drive for the crossfeed shaft 68021 the carriage 55., Further, details of thisgear'train-are believed to be unnecessary because the drive forthe present attachment-is taken from. said cross-feedshaft 66.. In the case of the present invention, the lead screw servesto drive the mechanism herein described which:is

- mounted on the carriage.

:For manually. moving the carriage independently of the lead screw 83 there is provided the usual hand feed wheel 61.functioning=' through a gear train in the apron E l -to rotate a pinion-1I along a rack 13,,the latter being. attached rigidly on the .lathe bed Thus, the carriage may L be: manually moved back and-forth. along the bed by means of the hand wheel 51, andithe lead screw 63 furnishes the drive to parts mountedon the carriage. The present apparatus being mounted upon the carriage 65, the drive therefor is picked 1 up at an extension 15 from the cross-feed shaft 66- .V v

- The shaftifilicarries apulley 11 fora quarterturn .beltdriveflfito pulley ill. The pulley 8i drivesa double reduction-gear 83 in a gear-box .85, the latter being attached to a main platen/'81;

The platen 81 is shown iwithoutsuperimposed parts -in.,Fig. 11.

The platen isifastened at 84 to an angle support 88 which in-turn is: carried upon the carriage, and is adjustableilniposition thereon; 'The purpose 'of .the anglesupport is tolset the platen 81 into a position which will place the box 85 clear'of thelathe bed.

- Adjustmentforfithe assembly of the unit 81,

88 is obtained by means of thetwo sets of rightangularly located set screws 89 threaded through behaped-members 90 at opposite cornersof the 7 support 88. The -members. 90 are attached to the carriage 65.- Itwill be seen that by means of the set screws 89 the support 88 andattached platen 81 may bemoved longitudinally,laterally,

and angularly- Itis heldlin any given adjusted position by means of. locking and elevating-studs 9I and 93. The studs 9|v work in'compression and the studs 93 in tension, havingheads 95 loosely located in TIT-slots 91'. The .fit between the heads 95 and the T-slots 91 is loose enough to accommodate the angular motion needed for making centeringadjustments, as follows:

In order to set the platen. 81, twoholes 89 and II'II are established thereon for accommodatingdowel pins I02 (Figs. 11 and 12). The

. points 99 and HM at the start of a cut lieupon the center line of thedesired .paraboloid. The point 99 is establishedat what is to become the focusF-2, and the'point IIII is established at the vertex V of a parallel paraboloid such as PinFigs.land:2.'- a J A jig I03-havingholes I85 is applied to the platen81 on the pins'I82 and establishes linear points I81 and: I89 on the same line as points P2 and V. The platen support 88 and platen 81 are then adjusted as a unit so that the. point I89 is at.- the exact center of the livespindle and isat apoint which will become the actual vertex of the actuallparaboloid; The point I01 is placed -at'the point-of the center III in the tail: stock II3. By this means the desired point of real focus 31-2 is established on the'center line ofthelathe; After adjustments for the platen are made; itis tightened down and the jig I03isremoved. .f

The'parts carried upon the platen 81 consist of the driving shaft H5, splined for example at four slots II1, and adapted to be keyed at IIB by means of one of saidslots- II1 to one of five Slots'J I 9 in a bell-crank I2I. The choice of four slots H1 in the shaf-tII5. and; five slots H9 in the bell-crankJI2-Iallows fora large number of 3 keyed relative adjustments vbetweenuthe bellcrankfll and theshaft I I5.

At Hand 29 are-shown the right-angular slots in platen 81 f0r:.accommodating-thecoordinator blocks 25 and3l respectively. i

The armsof the bell-crank I2I are phasedat ninety degrees as shown. The bell-crank is pivoted at I23 to a connecting rod I25 which in turn is pivoted at I21 to the slider 25 (see also Figs. '7 and 8). Thus, it will be seen that there is substituted for the screw-operation of block 25 the bell-crank 'I2I with the connecting rod To obtain a connection between the radius rod I9 and the pin 23 a slot I29 is employed, but it is" relied upon for-clearance and not for guiding. "This is to increase accuracy, there being'a shoe I3I formed around the pin 23which has guide surfaces I33 on'theroutside of. the radius'rod- I9.- a more accuratebeari'ng 'is'obtained, but the motionis equivalent to that indicated in the kinematic diagram (Fig. 3) at "numerals2l, 23.. v Q 1 1 In order to operatethe slide 3 I there is. pro.- -videda second arm Chef/he. belt-crank al 2 I phased,

at ninety degrees, which i pivoted at. I35 toia 7 connecting rod I31 which in turn is pivoted at I39 to the second sliding block 3|. The sliding block in Figs. 4 and 6 is of triangular form and has a dove-tailed connection on its bottom with the platen 81 at the guide 29 (see Fig. 9).

Since the pins I35 and I23 of the bell-crank I2l have a crank phase of ninety degrees, and since they work sliders 25 and 3| at a ninety degree angle, the displacements of said sliders are always proportional. Other schemes may be employed .for obtaining this proportional movement besides the screw mechanism shown .in Fig. 3 and the phased slider-crank mechanism of'Fig. 4. The screw mechanism has one advantage however, and that is uniformity of motion as well as proportionality.

The tool support 33 has a dove-tailed slide connection with the slider 3|. The relative sliding possible may be seen by comparing Figs. ,4 and 6 (see also Fig. 9)

The practical manner of mounting the swinging tool block M is .best indicated in Fig. .6 wherein said block will be seen to have an arcuate shaped end bearing portion I4I having a dove-tailed bearing connection I43 with the tool support 33 (see also Fig. 9). The purpose of this is to obtain a rotary connection between the tool block 4| and the tool support 33 which shall have a virtual center at C-P, which is the theoretical point above discussed on the tool. The tool itself consists of a small block of suitably hard cutting material, numbered I45 and held rigidly in position on the tool block 4| by means of a clamp bolt I4]. In order to maintain the tool block M as rigid as possible in all of its rotary positions, the tail is provided with a tongue I49 which rides in .a slot I5I of a guide I53, the latter forming a part of the tool support 33.

The drag link 5I which is shown with an offset (to effect clearances) is slotted asshownat 1 5 to slide on a pin block I 51 at the focus ,F,+2. The

center line of the slot I55 passes through the point and focus F-2.

The end of the drag link I near the tool I45 is also arcuately dove-tailed with respect to 33,- as shown at I59, to effect arota-ry relationship between the drag link 5i and the tool support 33. This is done indirectly, without obtaining interference from other parts, by making the slotted connection as shown at I59 withthe tool bar 4|, which, it is clear, is the equivalent of adirect rotary connection with the tool support 33. The center of curvature of the dove-tailed, slotted connection I59 also is the point C-P on the face of the tool I45.

To maintain the tool I45 normal to the surface being cut, the bisector links 5'! and 59 are used, the former being pivotedto the tool support 33 at I53 and the latter to the drag links 5I at I55. The two bisector links 51 and 59 are joined at a pin I61 which rides in a slot I53 of the tool bar M. The center line of the slot 63 also passes through the point C-:-P.

Fig. 9 makes clear how the dove-tailed connections I43 and I59 are on-opposite sides of the tool bar 4| so as to avoid interference between the two. This figure also clarifies the steadying bearing I51. It also indicates that the pin block I51 at the focus F2 is supported upon a. C;-.shaped member I'Il, which in turn is supported on the platen 81. order to clear and accommodate the tool holder '33 in the centerediposition of the latter (see also The member I II hasa C-shape in pins I3 and I13 disappears.

To operate the device, the jig I03 is first applied to the platen 81, after the parts above described have been removed (Figs. 11 and 12). This is done by applying the holes I35 to the pins I52 at the focal point F2 and vertex V. The focal point F-2 is that of the actual curve which is cut, and the vertex V is that of the equivalent-parallel parabola P. Then adjustments are made so that the platen 81 is moved to bring the jig points I01 and I09 into line respectively with the point of the lathe tail stock center III and the center of the live spindle 53. The jig is then removed, and the parts shown in Figs. 4 and 6 are applied.

It will be understood that the angle of the platen 81 may be other than as shown, or the de vice may even be horizontahthe criterion bein simply that the tool works in a plane which includes the longitudinal axis of the desiredparabola.

After the parts are mounted and set into the centered position shown in Fig. 4, the entire carriage 65 is manually moved forward by means of wheel 61 until the tool I45 assumes a depth of penetration desired into 51 for the depth of cut to be used. Rotation of the live spindle 53 will then result in causing turning of the material 57 with a drive through the gear BI to the lead screw 63. The lead screw drives through'the gears in the apron 64 to rotate the cross-feed shaft 66 and hence to drive the gear reduction unit through the quarter-turn belt I9. This causes movement of the linkage from the position shown in Fig. 4 to that shown in Fig. 6, the lateral traversebeing slow enough toefiect a desirable feed.

At numeral I8I is shownan oil sump for containing cutting oil, with a suction pipe I 83 leading to a pump I85 driven from a belt drive I81 from the live spindle. A flexible hose I89'leads to a nozzle I9I which is caused to project cutting lubricant upon the tool as it advances. It is clear that the nozzle I9I may be manually controlled to follow the tool, or connected with the tool.

The following will serve to indicate the scope that is intended for claims that follow: A parabola may be thought of as an especial case of an ellipse or a hyperbola. One of the conjugate foci of the parabola is at infinity, the other focus being that at F2. An ellipse happens to haveboth conjugate foci finite, as also does the hyperbola. In all three cases of the parabola, ellipse and hyperbola, lines drawn from the fool to any point on the curve will determine an angle Q, the bisector G of which. is a normal to the tangent of the curve at that point.

Thus, in Fig. 3, the center line of the tool holder 33 passes through the point CP and to a focus point at infinity (not shown), 'and'the center line of the drag link 5| passes through the finite locus F2 and. the point C--P. The center 'line'of the tool block 4| is the bisector and'ls'normal to the .tangent to the curve at point C--P.

Thus, the center line of the link 5f is parallel to alight ray which would emerge from a point source of light. at F'2, and the centerline of the tool support 33 is, parallel to the emerging direc- The amount of advance of the tool along the parabola P2 per revolution of the work on the live spindle of the lathe is arranged; by means-of the gear reduction unit 83, 85 in view of the curvature of the tool face, that only the most inconsequential, if any, ridges are left.

Curve generating systems of the class herein described, involving linkages which inherently produce the desired results, are to-be distin-.

said constant aspect of the tool.

The radius of curvature at the tip of the tool 145 should be less than the minimum radius of curvature of the curve which is bein cut.

several objects of the invention are achieved and other advantageous results attained.

As many changes could be made in the above constructions without departing from the scope of the invention as set forth in the claims, it is intended that all matter contained in the above description or shown in the accompanying draw- It'is the constant arrangement of a traverse movement with respect to said axis,

the toolbeing rotary with respect to the support about said point on the tool, a link also rotary with respect to said support about said point, a sliding arrangement for said link with respect to the focal point of the section line, and a propor- 'tioning means that may be usedyfor maintaining J In ,view of the above, it will be seen that the ings shall be interpreted as illustrative andnot in a limiting sense. A circle is not considere a conic section in the appended claims. 7

. I'claim; g 1. A section line generator for conic sections having a plurality of foci comprising a tool having a forming edge which includes a point'adapted to traverse the section, said tool having its forming edge lying substantiallyin the plane of the section, and means for maintainin constant an aspect between said edge and the section line during traverse, such that a line on the tool which is normal to the common tangent between the forming edge and the section line, and which passes through said point, shall always bisect the angle between lines passing from the point to said foci.

2. A section line generator for conic sections having a plurality of foci comprisinga cutting tool having a cutting edge of arcuate shape'and including a point adapted to traverse the sec.- tion, said tool having its cutting edgelying substantially in the plane of the section, and a linkage for maintaining constant an aspect between said edge and the section line during traverse, independently of templates or the like, such that a line on the tool which is normal to the common tangent between the forming edge and the section line, and which passes through said. point,

tioning linkage between the link and tool holder.

4. A parabolic section line generatorcomprising a tool having a smooth convex forming edge in whichis a point adapted to traverse the section, :a support for the tool having movementrangement for said link with respect to the focal point of the parabolic'section, and a bisecting linkage between the link and tool holder to maintain'the tool in a predetermined bisecting position between said holder and link.

5. A parabolic section line generator comprising a tool having a forming edge in which is a point adapted to traverse the section, a support for the toolhaving movement along a line passing through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding block slidingly supporting the tool holder for its longitudinal movement, a longitudinally sliding" block, aradial arm pivoted at the vertex ofa parallel parabola and having a slide connection with the last-named block, and also a connection'with the tool holder to control its longitudinal movement.

6. A parabolic section line generator comprising a tool having'a smooth convex forming edge in which isa point adapted to traverse the sec- -tion, a support for the tool having movement along a line passing through said point and parshall always bisect the angle between lines pass- I ing from the pointto said foci. l V I 3. A generator for section'lines having-fool, comprising a tool having a forming edge, in which is a point adapted to, traverse a line, av support for the tool having a line passing through said point and parallel to the axis of the section line,

means for giving the support a longitudinal and ing the support a longitudinal and atraverse movement with respect to said axis comprising a transversely sliding block slidingly supporting the tool holder for its longitudinal movement, a longitudinally sliding block, a radial arm pivoted at the vertex of a parallel parabola and having a;slide. connection with the last-named block and also a slide connection with the tool holder to control its longitudinal movement, and means.,for maintaining a predetermined aspect between said convex forming edge and the section line. h

. 7. A parabolic :section linegeneratorcomprismg a tool havingv a forming edge in which is a I point adapted to traverse the.section,.a support for the toolmovable along a line passing through said point and parallel to the axis of the parabola, means for giving the support .a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding'block slidingly guiding the, tool holder for its longitudinal move- ,ment, a longitudinal sliding block, a pivoted arm having a slide connection with the. last-named .blockand also a slide connection with'thetool I holder to control its longitudinal movement,.and means for proportionally moving said blocks, the transversely sliding block providing transverse mo,vemen t of the tool holder. f f 1 8., A parabolic section line generator comprising a tool having'a forming edge in ,which is a point adapted to traverse the section, "a support for the tool movable along a line passing through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding block slidingly guiding the tool holder for its longitudinal movement, a longitudinal sliding block, a pivoted arm having a slide connection with the last-named block and also a slide connection with the tool holder to control its longitudinal movement, and means for proportionally moving said blocks, comprising a double slider-crank mechanism having connections with the sliders which are phased at ninety degrees.

9. A parabolic section line generator comprisdinal sliding block, a pivoted radial arm having a slide connection with the last-named block and also a connection with the tool holder to control said longitudinal movement, the tool being rotary with respect to the support about said point on the tool, a link alsorotary with respect to said support about said point, a sliding arrangement for said link with respect to the focal point of the parabola, and a bisecting linkage between the link and the tool holder to maintain the tool in a predetermined bisecting position between said holder and link.

10. A parabolic section line generator comprising a tool having a smooth convex forming edge in which is a point adapted to traverse the section, a support for the tool having motion along a line passing through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding bl'ock slidingly guiding the tool its longitudinal movement, means for proportionally moving said blocks, the tool being rotary with respect to the support about said point on the tool, a link also rotary with respect to said support about said point, a sliding arrangement for said link with respect to the focal point of the parabolic section, and a bisecting linkage between the link and tool holder to maintain the tool in a predetermined bisecting position between said holder and link.

11. A parabolic section line generator comprising a tool having a smooth convex forming edge in which is a point adapted to traverse the section, a support for the tool having movement along a line passing through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding block slidingly guiding the tool in its longitudinal movement, a longitudinal sliding block, a radial arm pivoted at the vertex of a parallel parabola and having a slide connection with the last-named block and also a slideconnection with the tool holder to control its longitudinal movement, means for proportionally moving said blocks, comprising a double slidercrank mechanism having connections with the sliders phased at ninety degrees, the tool being rotary with respect to the support about said point on the tool, a link also rotary with respect to said support about said point, a sliding arrangement for said link with respect to the focal point of the parabola, and a bisecting linkage between the link and the tool holder to maintain the tool in a predetermined bisecting position between said holder and link.

12. A parabolic section line generator comprising a tool having a forming edge in which is a point adapted to traverse the section, a support for the tool having motion along a line passing through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding block slidingly guiding the tool holder in its longitudinal movement, a longitudinal sliding block, a pivoted arm having a slide connection with the last-named blockand also a sliding connection with the tool holder to control its longitudinal movement, means for proportionally moving said blocks, comprising a double slider-crank mechanism having connections with the sliders phased at ninety degrees.

13. A parabolic section line generator comprising a tool having a forming edge in which is a point adapted to traverse the section, a support for the tool having motion along a line passing 1, through said point and parallel to the axis of the parabola, means for giving the support a longitudinal and a traverse movement with respect to said axis comprising a transversely sliding block slidingly guiding the tool holder in its longitudinal movement, a longitudinal sliding block, a pivoted arm having a slide connection with the last-named block and also a sliding connection with the tool holder to control its longitudinal movement, means for proportionally moving said blocks, comprising geared screw connections with said blocks.

14. Apparatus for generating conic sections having two foci, comprising a tool support having a line passing through successive points on the section and through one focus, a rotary tool on the support movable about said successive points on the section as centers, a rotar drag link on the support also movable about said points as centers, said drag link having a sliding relationship with respect to means at the other focus, and a bisecting mechanism between the holder and the drag link adapted to maintain the tool at predetermined positions between said lines.

15. Apparatus for generating conic sections having two foci, comprising a tool support having a line passing through successive points on the section and through one focus, a rotary tool on the support movable about the successive points on the section as centers, a rotary drag link on the support also movable about said points as centers, said drag link having a sliding relationship with respect to center means at the other focus, a bisecting mechanism between the holder and the drag link adapted to maintain the tool at a predetermined bisecting position between said lines, said bisecting mechanism comprising a slot associatedwith the tool, the slot having a center line passing through said point on the section, slide means in said slot, and links of equal lengths pivoted at the same point to said last-named slide means and-at their other ends to the tool support and drag link respectively on ,13 lines which always cross on said successive points on a section. V

16. Means for centering a device of theeclass described on a lathe bed,;comprising an adjustable support on the bed, a jig adapted to be supported upon the support and having two gauging points, said jig being adapted to be placed on the support with said points being located on the same line with a hypothetical focus point and a hypothetical vertex point of a section to be made.

1'7. Means for centering a device of the class described on a lathe, comprising a support on the bed having rotary, vertical and lateral adjust: ments, a jig adapted to be supported upon the,

platen and having two gauging points,,said jig,

being adapted'to be placed on the platen with said points being located on the same line with a hypothetical focus point and a hypothetical vertex point of a conic section to be made, said platen being adjustable as to any of said adjustments to bring the gauge points on the jig into alignment with the center line of the jig.

, 18. In apparatus of the class described, a

linkage to be driven, a shaft having a driving 14 connection with said linkage, said driving connection comprising related splined members, one of which has an even number of splinesand the other an odd number of splines, and a single key efiecting a connection between a single pair of said splines.

20. In combination, a driving element provided with slots, a driven element provided with slots having different displacement from the driving element, and a key engaging one slot in the driving element and one slot in the driven element, said key being removable and replaceable in other slots of the driving and driven elements to I secure accurately phased, positive, and variable connection between the driving and driven elements.

21. In a kinematic chain for generating a parabola, a base, a straight bar pivoting on a point in said base, means revolving said bar about said point, a slider, and means moving said slider along said bar as said bar revolves so that a predetermined point on said slider traces a parabolic path relative to the base.

22; A conic section line tracer comprising a forming tool having a forming edge including a point adapted to traverse the section, said forming tool having its forming edge lying substantially in the plane of the section, and means for maintaining constant a predetermined aspect between said edge and the section line during traverse.

CHARLES B. MADDOCK. 

